I have a differential equation as follows and have got no idea how to solve it. Any help would be appreciated.
$$ \frac{d^2t}{dx^2} -2 (\frac{dt}{dx} )^2\frac{1}{t} = 0 $$
2026-03-27 01:43:50.1774575830
Method to solve this non-linear differential equation
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$$t''-2\frac{(t')^2}{t}=0 \iff \frac{t''}{t'}=2\frac{t'}{t}$$ Now you can integrate in both side and get $$\log|t'|=2\log|t|+\tilde C\iff t' = C\cdot t^2$$ and you can finish from here.